The average age of a group of 35 persons was 52 years. Five persons left the group and due to this the average age of the remaining persons in the group increased by 3 years. What is the average age (in years) of the persons who left the group?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 34
An average times the number of persons gives the total age. The total age of those who left is the old total minus the new total.
Total age of the 35 persons: \(35\times52=1820\) years
30 persons remain, with average \(52+3=55\): total \(30\times55=1650\) years
Total age of the 5 who left: \(1820-1650=170\) years
Their average: \(\displaystyle \frac{170}{5}=34\) years
Shortcut:
Each of the 30 who stayed is now 3 years above the old average of 52: together \(30\times3=90\) years above it
Those 90 years were made up by the 5 who left being below 52: \(\frac{90}{5}=18\) years each
Their average: \(52-18=34\) years